Finite Group Databasebeta

← #30600137

Subgroups — #30600137

Order 15616.

534 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462348C211yesmaximal, characteristic
2#21461997C211yesmaximal, characteristic
3#21461997C211yesmaximal, characteristic
4D61⋊#332C211yesmaximal, characteristic
5#21460654C211yesmaximal, characteristic
6#21460654C211yesmaximal, characteristic
7#487×D61C211yesmaximal, characteristic
8C2×Q8×#6923—21no—
9D61⋊(C4⋊C8)C2211yescharacteristic
10D61⋊(C4⋊C8)C2211yescharacteristic
11(C2×#6923)⋊Q8—21no—
12#16840713—21no—
13#16840711—22no—
14C4⋊C4×#6923—21no—
15C4×C4⋊#6923C2211yescharacteristic
16C4×C4⋊#6923C2211yescharacteristic
17#16840635—21no—
18#16840635—21no—
19#16840635—21no—
20#16840635—21no—
21#16840621—22no—
22C4⋊Q8×D61C2211yescharacteristic
23C4⋊Q8×D61C2211yescharacteristic
24#16840114C411yescharacteristic, complemented
25#16840113C411yescharacteristic, complemented
26#16840112C411yescharacteristic, complemented
27#16840111—22no—
28#103×D61—22no—
29C4×C8×D61C2211yescharacteristic
30C61×#487C411yescharacteristic, complemented
31C2×D61⋊C8—21no—
32C2×D61⋊C8—21no—
33Q8×#6923—42no—
34Q8×#6923—42no—
35C2×C4⋊#6923—22no—
36C2×C4⋊#6923D411yescharacteristic
37C2×C4⋊#6923D411yescharacteristic
38C2×C4⋊#6923D411yescharacteristic
39C2×C4⋊#6923D411yescharacteristic
40C2×C4×#6923—22no—
41C2×C4×#6923—21no—
42C2×C4×#6923—21no—
43#14519844—21no—
44#14519844—21no—
45C4⋊#92420—21no—
46C4⋊#92420—21no—
47(C2×#6923)⋊C4—22no—
48(C2×#6923)⋊C4—22no—
49(C2×#6923)⋊C4—21no—
50(C2×#6923)⋊C4—21no—
51C2×Q8×D61—21no—
52C2×Q8×D61—21no—
53C2×C8×D61—21no—
54#14519777C2×C411yescharacteristic
55#14519777C2×C411yescharacteristic
56#14519776—21no—
57#14519776—21no—
58#14519776—21no—
59#14519776D412yes—
60#14519775—21no—
61#14519775—21no—
62C4⋊C4×D61—21no—
63C4⋊C4×D61—21no—
64C4⋊C4×D61—21no—
65C4⋊C4×D61D412yes—
66C42×D61C2311yescharacteristic
67#14519702—22no—
68#14519701—22no—
69#14519700—22no—
70C4×#92418C2×C411yescharacteristic
71C8×Dic61—21no—
72C4⋊Q8×C61C2×C411yescharacteristic
73C4⋊Q8×C61C2×C411yescharacteristic
74#103×C61—22no—
75C4×C8×C61C2×C411yescharacteristic
76C22×#6923—21no—
77C22×#6923—21no—
78C22×#6923—21no—
79C22×#6923—21no—
80C2×Q8×C61—21no—
81C2×Q8×C61—21no—
82Q8×D61—41no—
83Q8×D61—41no—
84Q8×D61—41no—
85Q8×D61—41no—
86Q8×D61—42no—
87Q8×D61—42no—
88C2×C4×D61—22no—
89C2×C4×D61—41no—
90C2×C4×D61C2×D411yescharacteristic
91C2×C4×D61C2×D411yescharacteristic
92C2×C4×D61C2×D411yescharacteristic
93C2×Dic122—21no—
94C2×Dic122—22no—
95C2×Dic122—21no—
96C2×Dic122—41no—
97C2×#92420—41no—
98C2×#92420—41no—
99C4⋊#6923—21no—
100C4⋊#6923—21no—
101C4⋊#6923—21no—
102C4⋊#6923—21no—
103C4⋊#6923—21no—
104C4⋊#6923—21no—
105C4⋊#6923—44no—
106C4⋊#6923SD1612yes—
107C4⋊#6923Q1612yes—
108C4×#6923—44no—
109C4×#6923—41no—
110C4×#6923—41no—
111C4×#6923—41no—
112C4×#6923—41no—
113D61⋊C8—41no—
114D61⋊C8—41no—
115D61⋊C8—41no—
116D61⋊C8—41no—
117C2×C8×C61—21no—
118C4⋊C4×C61—21no—
119C4⋊C4×C61—21no—
120C4⋊C4×C61—21no—
121C4⋊C4×C61C22⋊C412yes—
122C42×C61C22×C411yescharacteristic
123C4⋊Dic61—21no—
124C4⋊Dic61—21no—
125C4⋊Dic61—21no—
126C4⋊Dic61C22⋊C412yes—
127#11758196—22no—
128#11758196—22no—
129#11758196—41no—
130#11758196—41no—
131C4×Dic61C2×D411yescharacteristic
132C4×Dic61#4111yescharacteristic
133C4×Dic61#4111yescharacteristic
134C2×#92418—21no—
135C8×D61—41no—
136C8×D61—41no—
137C22×D61#12011yescharacteristic
138C2×#6923—22no—
139C2×#6923—22no—
140C2×#6923—41no—
141C2×#6923—41no—
142C2×#6923—41no—
143C2×#6923—41no—
144C2×#6923—41no—
145C2×#6923—41no—
146C2×#6923—41no—
147C2×#6923—41no—
148C2×#6923—41no—
149C2×#6923—41no—
150Q8×C61—42no—
151Q8×C61—41no—
152Q8×C61—41no—
153C2×C4×C61—22no—
154C2×C4×C61—41no—
155C2×C4×C61C2×C22⋊C411yescharacteristic
156C2×C4×C61C4×D411yescharacteristic
157C2×C4×C61C4×D411yescharacteristic
158C2×Dic61—22no—
159C2×Dic61—41no—
160C2×Dic61#12111yescharacteristic
161C2×Dic61#12111yescharacteristic
162C2×Dic61#12311yescharacteristic
163C4×D61—21no—
164C4×D61—21no—
165C4×D61—42no—
166C4×D61—42no—
167C4×D61—81no—
168C4×D61—81no—
169C4×D61C2×SD1611yescharacteristic
170C4×D61C2×Q1611yescharacteristic
171C4×D61#13511yescharacteristic
172C4×D61#13511yescharacteristic
173C4×D61AGL(1,ℤ/8)11yescharacteristic
174C4×D61#13711yescharacteristic
175C4×D61#13711yescharacteristic
176C4×D61#13711yescharacteristic
177Dic122—41no—
178Dic122—41no—
179Dic122—42no—
180Dic122—42no—
181Dic122—42no—
182Dic122—82no—
183#92420—81no—
184#92420—81no—
185C8×C61—41no—
186#92418—41no—
187#9065—611nomaximal, Sylow
188C22×C61#38611yescharacteristic
189C2×D61#45011yescharacteristic
190C2×D61#45111yescharacteristic
191C2×D61#45211yescharacteristic
192C2×D61#45211yescharacteristic
193C2×D61#45411yescharacteristic
194C2×D61#45411yescharacteristic
195#6923—42no—
196#6923—42no—
197#6923—81no—
198#6923—81no—
199C4×C61—21no—
200C4×C61—42no—
201C4×C61—81no—
202C4×C61C4×SD1611yescharacteristic
203C4×C61C4×Q1611yescharacteristic
204C4×C61#44011yescharacteristic
205C4×C61#44111yescharacteristic
206Dic61—21no—
207Dic61—42no—
208Dic61—81no—
209Dic61#46111yescharacteristic
210Dic61#46211yescharacteristic
211Dic61#46311yescharacteristic
212Dic61#46411yescharacteristic
213C2×#487—611no—
214#2365—611no—
215#1987—611no—
216#1987—611no—
217C2×#332—611no—
218#1279—611no—
219#1279—611no—
220C2×C61#187711yescharacteristic
221C2×C61#187811yescharacteristic
222C2×C61#188811yescharacteristic
223D61#163511yescharacteristic
224D61#163611yescharacteristic
225D61#163711yescharacteristic
226D61#163811yescharacteristic
227C2×C4⋊Q8—611no—
228C2×C4⋊Q8—611no—
229C2×C4×Q8—1221no—
230#487—611no—
231#487—611no—
232#487—611no—
233#487—1222no—
234#487#692311yescharacteristic, complemented
235C2×C4⋊C8—611no—
236C2×C4⋊C8—611no—
237C2×#103—1222no—
238C2×C4×C8—611no—
239#391—1221no—
240#389—1221no—
241#387—1222no—
242C4×C4⋊C4—611no—
243C4×C4⋊C4—611no—
244C4×C4⋊C4—1221no—
245#340—1221no—
246#340—1221no—
247#340—1221no—
248#340—1221no—
249#332—1222no—
250C61#906511yescharacteristic, complemented, Sylow
251C22×Q8—1221no—
252C22×Q8—1221no—
253C22×C8—1221no—
254C22×C8—1221no—
255C22×C8—1221no—
256C4⋊Q8—612no—
257C4⋊Q8—611no—
258C4⋊Q8—611no—
259C4⋊Q8—1221no—
260C4⋊Q8—1221no—
261C4⋊Q8—1221no—
262C4⋊Q8—1221no—
263C4⋊Q8—1221no—
264C4⋊Q8C2×#692311yescharacteristic
265C4⋊Q8C2×#692311yescharacteristic
266C4×Q8—2442no—
267C4×Q8—2442no—
268C2×C4⋊C4—611no—
269C2×C4⋊C4—611no—
270C2×C4⋊C4—612no—
271C2×C4⋊C4—611no—
272C2×C4⋊C4—611no—
273C2×C4⋊C4—1221no—
274C2×C4⋊C4—1221no—
275C2×C4⋊C4—1221no—
276C2×C4⋊C4—1222no—
277C2×C42—611no—
278C2×C42—1221no—
279C2×C42—1221no—
280C2×C42—1222no—
281C4⋊C8—1221no—
282C4⋊C8—1221no—
283C4⋊C8—1221no—
284C4⋊C8—1221no—
285#103—22no—
286#103—1222no—
287#103—1222no—
288#103—1222no—
289C4×C8—611no—
290C4×C8—1221no—
291C4×C8C2×#692311yescharacteristic
292#95—1221no—
293#95—1221no—
294#95—1222no—
295#95—1222no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—1222no—
299C2×Q8—1221no—
300C2×Q8—1221no—
301C2×Q8—2441no—
302C2×Q8—2441no—
303C2×Q8—2441no—
304C2×Q8—2441no—
305C2×Q8—2441no—
306C2×Q8—2442no—
307C2×Q8—2442no—
308C22×C4—611no—
309C22×C4—611no—
310C22×C4—611no—
311C22×C4—1222no—
312C22×C4—1221no—
313C22×C4—1221no—
314C22×C4—1221no—
315C22×C4—1221no—
316C22×C4—2441no—
317C2×C8—21no—
318C2×C8—1221no—
319C2×C8—2441no—
320C2×C8—2441no—
321C2×C8—2441no—
322C2×C8—2441no—
323C2×C8—2441no—
324C2×C8—2441no—
325C2×C8—2441no—
326C2×C8—2441no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—612no—
331C4⋊C4—612no—
332C4⋊C4—612no—
333C4⋊C4—1222no—
334C4⋊C4—1222no—
335C4⋊C4—1221no—
336C4⋊C4—1221no—
337C4⋊C4—1221no—
338C4⋊C4—1221no—
339C4⋊C4—1221no—
340C4⋊C4—1221no—
341C4⋊C4—1221no—
342C4⋊C4—1221no—
343C4⋊C4—1221no—
344C4⋊C4—2441no—
345C4⋊C4—2441no—
346C4⋊C4—2444no—
347C4⋊C4C22⋊#692312yes—
348C42—611no—
349C42—611no—
350C42—611no—
351C42—2441no—
352C42—2441no—
353C42—2441no—
354C42—2441no—
355C42—2444no—
356C42C22×#692311yescharacteristic
357C23—611no—
358Q8—42no—
359Q8—41no—
360Q8—41no—
361Q8—4882no—
362Q8—2442no—
363Q8—2442no—
364Q8—2442no—
365Q8—2441no—
366Q8—2441no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—611no—
370C2×C4—611no—
371C2×C4—611no—
372C2×C4—611no—
373C2×C4—611no—
374C2×C4—611no—
375C2×C4—611no—
376C2×C4—611no—
377C2×C4—611no—
378C2×C4—611no—
379C2×C4—611no—
380C2×C4—1221no—
381C2×C4—1221no—
382C2×C4—1222no—
383C2×C4—1222no—
384C2×C4—1222no—
385C2×C4—4881no—
386C2×C4—4881no—
387C2×C4—2442no—
388C2×C4—2442no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4—2441no—
392C2×C4—2441no—
393C2×C4—2441no—
394C2×C4—2441no—
395C2×C4—2441no—
396C2×C4—2441no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4C2×C22⋊#692311yescharacteristic
401C2×C4D4×#692311yescharacteristic
402C2×C4D4×#692311yescharacteristic
403C8—41no—
404C8—4881no—
405C8—4881no—
406C8—2441no—
407C22—611no—
408C22—611no—
409C22—611no—
410C22—611no—
411C22—611no—
412C22—611no—
413C22#1684071011yescharacteristic
414C4—21no—
415C4—42no—
416C4—81no—
417C4—611no—
418C4—611no—
419C4—611no—
420C4—611no—
421C4—1221no—
422C4—4881no—
423C4—4881no—
424C4—4881no—
425C4—2442no—
426C4—2442no—
427C4—2442no—
428C4SD16×#692311yescharacteristic
429C4Q16×#692311yescharacteristic
430C4#1684080111yescharacteristic
431C4#1684080211yescharacteristic
432C2—611no—
433C2—611no—
434C2—611no—
435C2—611no—
436C2#2146181211yescharacteristic
437C2#2146181311yescharacteristic
438C2#2146182711yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#487C4
socleC22×C61#386
prime radicalC22×D61#120
cosocleC42×D61C23
hypercenter#487#6923
hypocenterC61#9065
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
24. #16840114C4semidirect
25. #16840113C4semidirect
26. #16840112C4semidirect
30. C61×#487C4semidirect
234. #487#6923semidirect
250. C61#9065semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214623482
#214619972
D61⋊#3322
#214606542
#487×D612
#906561